A classification of finite simple amenable Z-stable C*-algebras, II, --C*-algebras with rational generalized tracial rank one

TL;DR

This paper provides a classification theorem for a broad class of unital simple separable amenable Z-stable C*-algebras, covering all possible Elliott invariants for such algebras with finite rational tracial rank.

Contribution

It establishes a comprehensive classification for unital simple separable amenable Z-stable C*-algebras with finite rational tracial rank, extending the understanding of their structure.

Findings

Classification theorem for Z-stable C*-algebras with finite rational tracial rank

Includes all unital simple separable amenable C*-algebras satisfying UCT

Exhausts all possible Elliott invariants for this class

Abstract

A classification theorem is obtained for a class of unital simple separable amenable Z-stable C*-algebras which exhausts all possible values of the Elliott invariant for unital stably finite simple separable amenable Z-stable C*-algebras. Moreover, it contains all unital simple separable amenable C*-algebras which satisfy the UCT and have finite rational tracial rank